A vector bundle proof of Poncelet's closure theorem

Jean Vallès (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

There are few different proofs of the celebrated Poncelet closure theorem about polygons simultaneously inscribed in a smooth conic and circumscribed around another. We propose a new proof, based on the link between Schwarzenberger bundles and Poncelet curves.

Mots clés: Darboux theorem; Schwarzenberger bundles; Poncelet curves; Inscribed and circumscribed conics; Poncelet porism; Schwarzen-berger bundles

Domaines: Géométrie algébrique [math.AG]

Jean Vallès. A vector bundle proof of Poncelet's closure theorem. Expositiones Mathematicae, 2012, 30, pp.399-405. ⟨10.1016/j.exmath.2012.08.009⟩. ⟨hal-00664308v2⟩